Techniques for 3-D modeling of objects through observation have been extensively investigated. Such 3-D modeling has a wide range of applications including virtual reality and object recognition. Three-dimensional (stereo) imaging of surfaces by reflected light have been studied performed by several methods, as illustrated in FIG. 5. Binocular stereo imaging is an old, established technique. In binocular imaging, two sets of two-dimensional information (e.g., two-dimensional images) from the surface measured from two different viewpoints at a distance apart.
Another technique illustrated in FIG. 5 is polarimetric stereo imaging. Polarimetry is the measurement and interpretation of the polarization of transverse waves; generally electromagnetic waves, such as radio or light waves. Polarimetry may be done on electromagnetic waves that have traveled through or have been reflected, refracted, or diffracted by some material in order to characterize that object.
Photometric stereo imaging by reflected light has been studied, for example by J. R. A. Torreão and J. L. Fernandes, “Matching photometric-stereo images”, J. Opt. Soc. Am. A15(12), 2966-2975 (1998). Photometric stereo imaging of reflected light uses more than one two-dimensional set of information, measured using reflected light with a wavelength spectrum that varies with the direction of transmitter or receiver. One such transmitter is solar radiation scattered by the atmosphere on a clear day. Another method, using polarimetric reflectance, has also been used for stereo imaging. In polarimetric reflectance, stereo information is determined from sequential measurements of reflectance at different polarization for transmitter or receiver.
Various articles have been written on the spatial arrangement of objects and depth perception. In the publication by B. K. P. Horn and B. G. Schunk, “Determining Optical Flow”, MIT Artificial Intelligence Laboratory, 572, 0-27 (1980), hereby incorporated by reference, there is a description of a method for finding optical flow. Optical flow is defined in the article as:                Optical flow is the distribution of apparent velocities of movement of brightness patterns in an image. Optical flow can arise from relative motion of objects and the viewer [citation omitted]. Consequently, optical flow can give important information about the spatial arrangement of the objects viewed and the rate of change of this arrangement [citation omitted]. Discontinuities in the optical flow can help in segmenting images into regions that correspond to different objects.        
According to the “Determining Optical Flow” article, in general optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented in the “Determining Optical Flow” article which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm used in “Determining Optical Flow” article reportedly can handle image sequences that are quantized rather coarsely in space and time and is, reportedly, insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
As used herein, the terminology “optical flow” encompasses taking an image of the same scene using different polarizations such that there is an apparent change of intensity from one image to another, such that a vector or vectors may be used to show the apparent movement, which is a representation of the optical flow.
These methods of stereo imaging with reflected radiation have limitations in practice. Reflected radiation contains little information on chemical composition of the surface, regardless of stereo information. Photoemission spectra have long been used to partially determine chemical composition of a surface. Binocular stereo cannot extract three-dimensional information for large distances. Photometric stereo requires the source of illumination to arrive at the surface from more than one direction, each direction having a different wavelength spectrum. Therefore, photometric stereo imaging with reflectance does not function when there is no transmitter available with a spectrum that varies with angle. For example, photometric stereo imaging with solar radiation cannot be used either at noon or on severely overcast days to determine stereoscopic information. Furthermore, the spectroscopic and stereoscopic information cannot be simultaneously extracted with photometric reflectance stereo imaging.
Polarimetric reflectance can be used to extract some three-dimensional information from a surface, e.g. D. Miyazaki et al., “Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths,” J. Opt. Soc. Am. A 19, 687-694 (2004). The polarization state, emitted by the transmitter or sensed by the receiver, is varied with time. The variations in signal intensity are also measured at various times and correlated with polarization. However, a unique three-dimensional image by specular reflected radiation cannot be uniquely determined with polarimetric reflectance. A method using two different receiver angles for the illuminating radiation in addition to changing polarization has been developed, but has some of the same problems as binocular reflectance imaging. See D. Miyazaki et al., “Transparent Surface Modeling from a Pair of Polarization Images,” IEEE Trans. Patt. Anal. Mach. Intel. 26, 73-82 (2004).
Thus, there exists a need for a remote sensing method of monocular (i.e., single view) stereo imaging without a uniqueness problem for stereo images, yet with a partial chemical selectivity. A method of monocular stereo imaging could have greater effective range for determining the unique three-dimensional shape of a surface than a binocular stereo method, and would be simpler with respect to detection aperture.